Question

1 soda + 1 cupcake+1popsicle=$22.00

1 soda +3cupcakes+3popsicle=$40.00
if a cupcake cost,$2:00 more than a popsicle,find the cost of the following

a)1 cupcake

b)1 popsicle ​

Answer 1

a) 1 cupcake = $5.50

b) 1 Popsicle = $3.50

Explanation:

Let s = cost of one soda

Let c = cost of one cupcake

Let p = cost of one Popsicle

From the given information we can create 3 equations:

• Equation 1: s + c + p = 22
• Equation 2: s + 3c + 3p = 40
• Equation 3: c = p + 2

Subtract Equation 1 from Equation 2 to eliminate the variable s:

s + 3c + 3p = 40

- s + c + p = 22

2c + 2p = 18

Substitute Equation 3 into this new equation and solve for p:

⇒ 2c + 2p = 18

⇒ 2(p + 2) + 2p = 18

⇒ 2p + 4 + 2p = 18

⇒ 4p = 14

⇒ p = 3.5

Substitute the found value of p into Equation 3 and solve for c:

⇒ c = p + 2

⇒ c = 3.5 + 2

⇒ c = 5.5

To find the cost of a soda (s), substitute the found values of p and c into Equation 1:

⇒ s + c + p = 22

⇒ s + 5.5 + 3.5 = 22

⇒ s = 13

Therefore,

• 1 soda costs $13
• 1 cupcake costs $5.50
• 1 Popsicle costs $3.50